Alternative results for option pricing and implied volatility in jump-diffusion models using Mellin transforms

Authors

Tianyu Li, University of WollongongFollow
Marianito R. Rodrigo, University of WollongongFollow

RIS ID

111404

Publication Details

Li, T. Ray. & Rodrigo, M. R. (2017). Alternative results for option pricing and implied volatility in jump-diffusion models using Mellin transforms. European Journal of Applied Mathematics, 28 (5), 789-826.

Abstract

In this article, we use Mellin transforms to derive alternative results for option pricing and implied volatility estimation when the underlying asset price is governed by jump-diffusion dynamics. The current well known results are restrictive since the jump is assumed to follow a predetermined distribution (e.g., lognormal or double exponential). However, the results we present are general since we do not specify a particular jump-diffusion model within the derivations. In particular, we construct and derive an exact solution to the option pricing problem in a general jump-diffusion framework via Mellin transforms. This approach of Mellin transforms is further extended to derive a Dupire-like partial integro-differential equation, which ultimately yields an implied volatility estimator for assets subjected to instantaneous jumps in the price. Numerical simulations are provided to show the accuracy of the estimator.